Beale, who was already playing with an injured left shoulder, suffered the latest injury during the Rebels' 31-26 loss to the New South Wales Waratahs on Friday.
He has fractured the third metacarpal in his left hand and has been ruled out for three to four weeks, the Rebels said in a statement on their website.
"Obviously I've got some time off now to try and focus on the shoulder and get that back to full strength," Beale said in the statement. "Hopefully when I do come back I'll hit the ground fit and ready."
